Simplify the following expression: $k = \dfrac{25a}{5a^2 - 35a}$ You can assume $a \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $25a = (5\cdot5 \cdot a)$ The denominator can be factored: $5a^2 - 35a = (5 \cdot a \cdot a) - (5\cdot7 \cdot a)$ The greatest common factor of all the terms is $5a$ Factoring out $5a$ gives us: $k = \dfrac{(5a)(5)}{(5a)(a - 7)}$ Dividing both the numerator and denominator by $5a$ gives: $k = \dfrac{5}{a - 7}$